Open AccessMeasure density and extendability of Sobolev functions
Author(s) -
Piotr Hajłasz,
Pekka Koskela,
Heli Tuominen
Publication year - 2008
Publication title -
revista matemática iberoamericana
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.569
H-Index - 52
eISSN - 2235-0616
pISSN - 0213-2230
DOI - 10.4171/rmi/551
Subject(s) - measure (data warehouse) , sobolev space , extension (predicate logic) , mathematics , metric (unit) , domain (mathematical analysis) , pure mathematics , sobolev inequality , mathematical analysis , computer science , data mining , operations management , economics , programming language
We study necessary and sufficient conditions for a domain to be a Sobolev extension domain in the setting of metric measure spaces. In particular, we prove that extension domains must satisfy a measure density condition.
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